The three-tangles \(\tau _3\)[1]} for \(\vert \psi _i \rangle \)  and concurrences[2]}, [3]} for the reduced mixed states are summarized in Table I. As Table I shows, \(U_{\mbox{oracle}}\)  transforms the
separable state \(\vert s \rangle \)  to \(\vert \psi _1 \rangle \) , whose three-tangle is \(1/4\) . Since maximum three-tangle is 1Maximal three-tangle is realized in the Greenberger-Horne-Zeilinger (GHZ) state[4]}
\(\vert GHZ \rangle  = \frac{1}{\sqrt{2}} (\vert 000 \rangle  + \vert 111 \rangle )\) 
and its local unitary transformed states.
, \(\vert \psi _1 \rangle \)  is only partially entangled state. Thus, maximal entanglement creation does not occur in this case.
\(U_{\mbox{diffuser}}\)  changes \(\vert \psi _1 \rangle \)  into \(\vert \psi _2 \rangle \) , whose three-tangle is \(1/16\) . Therefore, the complete annihilation of tripartite entanglement also does not occur. Same is true for \(\vert \psi _3 \rangle \)  and \(\vert \psi _4 \rangle \) .
Similar behavior occurs in the bipartite entanglement.
